Green’s Dictionary of Slang

tipsy, slightly drunk.

1694		French Rogue 25: [B]y his grunting, and fumbling for the Key under the Door, I perceiv'd he was somewhat sucky, or addle-Pated.
c.1698		B.E. Dict. Canting Crew n.p.: Suckey, drunkish, maudlin, half Seas o’er.
1725		New Canting Dict. [as cit. c.1698].
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. c.1698].
1754		Proc. Old Bailey 23 Oct. 313/1: The prisoner told him he had it of a suckey cull, and Mr. Fielding said, Ben, what is the meaning of that word? his answer was, he could not tell.
1768		Proc. Old Bailey 6 July 235/1: Said Craycraft, there is a sucking cull, that is, a drunken gentleman, go and ask him what he has got.
1781		G. Parker View of Society II 105: The old woman having been used to get a little sucky now and then.
1791		‘Flash Lang.’ in Confessions of Thomas Mount 19: Drunk, sucky.
1804		C.L. Lewes Comic Sketches 27: While others would say he [was], ‘Very much disguis'd — Clipp'd the King's English —Quite happy — Bosky—Fuddled — Muddled — Tipsy — Dizzy — Muzzy — Sucky’.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1857		Bell’s Life in Victoria (Melbourne) 21 Feb. 2/1: ‘Blindman’s Holiday’ means night [...] —‘Darkman’s’ is the same. ‘Suck’ means drink and ‘sucky’ means that stage of ebriety, called rather drunk.